A Minimal Deterministic Trading Rule for Complex Price Paths

Summary

The document describes a compact deterministic model in which an investor reacts to recent market moves. After two consecutive upticks or downticks a few ticks earlier, the rule signals a sale; otherwise, it signals a purchase. The proposed model is presented as the smallest deterministic construction capable of generating complex financial price behavior, with generalizations producing a wider variety of patterns.

Its stated evidence is a comparison with a random walk: the model is said to produce fatter-tailed returns and more frequent crashes, features that the authors regard as closer to real markets. It requires no parameter fitting. The excerpt does not specify the exact timing convention, asset data, evaluation procedure, or quantitative fit to observed markets, so the claimed realism cannot be assessed from this description alone. It presents a model of price-path generation, not a tested trading strategy with reported profitability.

Key ideas

• A simple deterministic rule maps recent runs of price moves into buy or sell decisions.
• The proposed model generates complex price paths without parameter fitting.
• Compared with a random walk, it is claimed to produce fatter tails and more frequent crashes.
• The excerpt gives no empirical validation details or evidence of trading profitability.

Tags

# The Minimal Model of Financial Complexity


# The Minimal Model of Financial Complexity









A representative investor generates realistic and complex security price paths by following this trading strategy: if, a few ticks ago, the market asset had two consecutive upticks or two consecutive downticks, then sell, and otherwise buy. This simple, unique, and robust model is the smallest possible deterministic model of financial complexity, and its generalization leads to complex variety. Compared to a random walk, the minimal model generates time series with fatter tails and more frequent crashes, thus more closely matching the real world. It does all this without any parameter fitting.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.